When tossing a coin, there are two possible outcomes: [i]heads [/i]or [i]tails[/i].[br][br]Since the [i]mathematical probability[/i] of an event is the [i]ratio [/i]between the [i]number [/i]of [i]favorable cases[/i] and the [i]number [/i]of [i]possible cases[/i], both the event ‘[i]heads occurs[/i]’ and the event ‘[i]tails occurs[/i]’ have probability 1/2.[br][br]Another way to measure the probability of an event is [i]empirical[/i]: the trial is [i]repeated [/i]several times, and the [i]relative frequency[/i] of the event is calculated. This is the [i]ratio [/i]between the [i]number [/i]of [i]times [/i]the [i]event occurs[/i] and the [i]number [/i]of [i]trials [/i]performed.[br][br]Use the app below to observe how, as the number of trials increases, the value of the [i]relative frequency[/i] of an event [i]approaches [/i]the [i]mathematical probability[/i] of the event.
You have a bag, containing a red marble and a blue marble.[br]You pick one of the marbles from the bag, take note of its color, and put the marble back in the bag. [br]What is the probability to extract a blue marble?[br]By repeating the experiment over and over, can you say that the empirical law of large numbers holds?[br]Explain your conjectures.
You now have a bag containing a red marble, a blue marble and a yellow marble.[br]You pick one of the marbles from the bag, take note of its color, and [i]don't[/i] put the marble back in the bag. [br]What is the probability to extract a blue marble?[br]By repeating the experiment over and over, can you say that the empirical law of large numbers holds in this case?[br]Explain your conjectures.